Non uniform stability for the Timoshenko beam with tip load

TL;DR

This paper analyzes the stability of a Timoshenko beam with a tip load, demonstrating polynomial decay under certain conditions when boundary controls are applied, accounting for rotary inertia of the load.

Contribution

It establishes polynomial decay rates for a hybrid Timoshenko beam model with tip load, including rotary inertia effects, under feedback boundary controls.

Findings

Polynomial decay achieved under equal speed wave condition.

Inclusion of rotary inertia in stability analysis.

Effective boundary feedback controls ensure stability.

Abstract

In this paper we consider a hybrid elastic model consisting of a Timoshenko beam and a tip load at the free end of the beam. Under the equal speed wave propagation condition, we show polynomial decay for the model which includes the rotary inertia of the tip load when feedback boundary moment and force controls are applied at the point of contact between the beam and the tip load.